RS Aggarwal 2019,2020 solution class 7 chapter 1 Integers Exercise 1B

Exercise 1B

Page-9

Question 1:

Multiply:

(i) 16 by 9
(ii) 18 by − 6
(iii) 36 by − 11
(iv) − 28 by 14
(v) − 53 by 18
(vi) − 35 by 0
(vii) 0 by − 23
(viii) − 16 by − 12
(ix) − 105 by − 8
(x) − 36 by − 50
(xi) − 28 by − 1
(xii) 25 by − 11

Answer 1:

(i) 16 $\times$ 9 = 144
(ii) 18 $\times$ (−6) = $-(18\times 6) =$−108
(iii) 36 $\times$ (−11) = $- (36\times 11) =$−396
(iv)  (−28) $\times$14 = $-(28\times 14) =$−392
(v) (−53) $\times$ 18 = $-(53\times 18) =$−954
(vi) (−35) $\times$ 0 = 0  
(vii) 0 $\times$ (−23) = 0
(viii) (−16) $\times$ (−12) = 192
(ix) (−105) $\times$ (−8) = 840
(x) (−36) $\times$ (−50) = 1800
(xi) (−28) $\times$ (−1) = 28
(xii)  25 $\times$ (−11) = $- (25\times 11) =$−275

Question 2:

Find each of the following products:

(i) 3 × 4 × (−5)
(ii) 2 × (−5) × (−6)
(iii) (−5) × (−8) × (−3)
(iv) (−6) × 6 × (−10)
(v) 7 × (−8) × 3
(vi) (−7) × (−3) × 4

Answer 2:

(i) 3 × 4 × (−5) = (12) × (−5) = −60
(ii) 2 × (−5) × (−6) = (−10) × (−6) = 60
(iii) (−5) × (−8) × (−3) = (−5) × (24) = −120
(iv)  (−6) × 6 × (−10) = 6 × (60) = 360
(v)  7 × (−8) × 3 = 21 × (−8) = −168
(vi)  (−7) × (−3) × 4 = 21 × 4 = 84

Question 3:

Find each of the following products:

(i) (−4) × (−5) × (−8) × (−10)
(ii) (−6) × (−5) × (−7) × (−2) × (−3)
(iii) (−60) × (−10) × (−5) × (−1)
(iv) (−30) × (−20) × (−5)
(v) (−3) × (−3) × (−3) × ...6 times
(vi) (−5) × (−5) × (−5) × ...5 times
(vii) (−1) × (−1) × (−1) × ...200 times
(viii) (−1) × (−1) × (−1) × ...171 times

Answer 3:

(i)  Since the number of negative integers in the product is even, the product will be positive.
    (4) × (5) × (8) × (10) = 1600
(ii) Since the number of negative integers in the product is odd, the product will be negative.
  −(6) × (5) × (7) × (2) × (3) = −1260
(iii) Since the number of negative integers in the product is even, the product will be positive.
   (60) × (10) × (5) × (1) = 3000
(iv) Since the number of negative integers in the product is odd, the product will be negative.
   −(30) × (20) × (5) = −3000
(v) Since the number of negative integers in the product is even, the product will be positive.
    $(-3{)}^6$ = 729
(vi) Since the number of negative integers in the product is odd, the product will be negative.
   $(-5{)}^5$ = −3125
(vii) Since the number of negative integers in the product is even, the product will be positive.
    $(-1{)}^{200}$= 1
(viii) Since the number of negative integers in the product is odd, the product will be negative.
     $(-1{)}^{171}$ = −1

Question 4:

What will be the sign of the product, if we multiply 90 negative integers and 9 positive integers?

Answer 4:

Multiplying 90 negative integers will yield a positive sign as the number of integers is even.
Multiplying any two or more positive integers always gives a positive integer.
The product of both(the above two cases) the positive and negative integers is also positive.
Therefore, the final product will have a positive sign.

Question 5:

What will be the sign of the product, if we multiply 103 negative integers and 65 positive integers?

Answer 5:

Multiplying 103 negative integers will yield a negative integer, whereas 65 positive integers will give a positive integer.
The product of a negative integer and a positive integer is a negative integer.

Question 6:

Simplify:

(i)(−8) × 9 + (−8) × 7
(ii) 9 × (−13) + 9 × (−7)
(iii) 20 × (−16) + 20 × 14
(iv) (−16) × (−15) + (−16) × (−5)
(v) (−11) × (−15) + (−11) × (−25)
(vi) 10 × (−12) + 5 × (−12)
(vii) (−16) × (−8) + (−4) × (−8)
(viii) (−26) × 72 + (−26) × 28

Answer 6:

(i) (−8) $\times$ (9 + 7)   [using the distributive law]
= (−8) $\times$ 16 = −128

(ii)  9 $\times$ (−13 + (−7))  [using the distributive law]
= 9 $\times$ (−20) = −180

(iii)  20 $\times$ (−16 + 14)    [using the distributive law]
= 20 $\times$ (−2) = −40

(iv) (−16) $\times$ (−15 + (−5))  [using the distributive law]
= (−16) $\times$ (−20) = 320

(v) (−11) $\times$ (−15 +(−25))  [using the distributive law]
= (−11) $\times$ (−40)
= 440

(vi) (−12) $\times$ (10 + 5)   [using the distributive law]
= (−12) $\times$ 15 = −180

(vii) (−16 + (−4)) $\times$ (−8)  [using the distributive law]
= (−20) $\times$ (−8) = 160

(viii) (−26) $\times$ (72 + 28)    [using the distributive law]
= (−26) $\times$100 = −2600

Question 7:

Fill in the blanks:

(i) (−6) × (......) = 6
(ii) (−18) × (......) = (−18)
(iii) (−8) × (−9) = (−9) × (......)
(iv) 7 × (−3) = (−3) × (......)
(v) {(−5)×3} × (−6) = (......) × {3×(−6)}
(vi) (−5) × (......) = 0

Answer 7:

(i) (−6) × (x) = 6
$x = \frac{6}{-6} = \frac{-6}{6}= -1$

Thus, x = (−1)

(ii) 1      [∵ Multiplicative identity]
(iii) (−8)      [∵ Commutative law]
(iv) 7         [∵ Commutative law]
(v) (−5)   [∵ Associative law]
(vi) 0    [∵ Property of zero]

Question 8:

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (−2) marks are awarded for every incorrect answer and 0 for each question not attempted.

(i) Ravi gets 4 correct and 6 incorrect answers. What is his score?
(ii) Reenu gets 5 correct and 5 incorrect answers. What is her score?
(iii) Heena gets 2 correct and 5 incorrect answers. What is her score?

Answer 8:

We have 5 marks for correct answer and (−2) marks for an incorrect answer.

Now, we have the following:

(i) Ravi's score = 4 $\times$ 5 + 6 $\times$ (−2)
= 20 + (−12) =8

(ii) Reenu's score = 5 $\times$ 5 + 5 $\times$ (−2)
= 25 − 10 = 15

(iii) Heena's score = 2 $\times$ 5 + 5 $\times$ (−2)
= 10 − 10 = 0

Question 9:

Which of the following statements are true and which are false?

(i) The product of a positive and a negative integer is negative.
(ii) The product of two negative integers is a negative integer.
(iii) The product of three negative integers is a negative integer.
(iv) Every integer when multiplied with −1 gives its multiplicative inverse.
(v) Multiplication on integers is commutative.
(vi) Multiplication on integers is associative.
(vii) Every nonzero integer has a multiplicative inverse as an integer.

Answer 9:

(i) True.
(ii) False. Since the number of negative signs is even, the product will be a positive integer.
(iii) True. The number of negative signs is odd.
(iv) False. a $\times$ (−1) = −a, which is not the multiplicative inverse of a.
(v) True. a $\times$ b = b $\times$ a
(vi) True. (a $\times$ b) $\times$ c = a $\times$ (b $\times$ c)
(vii) False. Every non-zero integer a has a multiplicative inverse $\frac{1}{a}$, which is not an integer.